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Quince clan: Difference between revisions

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**Imported revision 338028770 - Original comment: **
 
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
The '''quince clan''' [[Tempering out|tempers out]] the [[quince comma]], {{monzo| -15 0 -2 7 }} = 823543/819200. Quince temperaments include:
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-21 15:31:43 UTC</tt>.<br>
* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca|Starling temperaments]]
: The original revision id was <tt>338028770</tt>.<br>
* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
: The revision comment was: <tt></tt><br>
* ''[[Quincy]]'' (+4375/4374) → [[Ragismic microtemperaments #Quincy|Ragismic microtemperaments]]
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
* ''[[Birds]]'' (+3136/3125) → [[31st-octave temperaments #Birds|31st-octave temperaments]]
<h4>Original Wikitext content:</h4>
* ''[[Octowerck]]'' (+321489/320000 or 420175/419904) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]]
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
* [[Cotoneum]] (+10976/10935) → [[Garischismic clan #Cotoneum|Garischismic clan]]
* ''[[Countermiracle]]'' (+6144/6125) → [[Porwell temperaments #Countermiracle|Porwell temperaments]]


This tempers out quince, the no-threes comma |-15 0 -2 7&gt; = 823543/819200. Quince temperaments include miracle, quincy, octowerck and birds as well as the ones listed below.
== Mercy ==
Mercy is the no-3 version of miracle. It can be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of [[31edo]]. Two generators make an [[8/7]]; five generators make a [[7/5]].  


=Essence=
[[Subgroup]]: 2.5.7
Essence is of interest because of the abundant supply of essentially tempered chords.


Commas: 321489/320000, 823543/820125
[[Comma list]]: 823543/819200


POTE generator: ~243/196 = 372.597
{{Mapping|legend=2| 1 3 3 | 0 -7 -2 }}


Map: [&lt;2 10 27 23|, &lt;0 -11 -36 -28|]
: mapping generators: ~2, ~343/320
Wedgie: &lt;&lt;22 72 56 63 27 -72||
EDOs: 58, 190, 248, 438d, 686d
Badness: 0.1736


==11-limit==
{{Mapping|legend=3| 1 0 3 3 | 0 0 -7 -2 }}
Commas: 441/440, 8019/8000, 456533/455625


POTE generator: ~243/196 = 372.599
: gencom: [2 343/320; 823543/819200]


Map: [&lt;2 10 27 23 33|, &lt;0 -11 -36 -28 -42|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/320 = 116.291
EDOs: 58, 190, 248, 438d
Badness: 0.0464


==13-limit==
{{Optimal ET sequence|legend=1| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }}
Commas: 441/440, 729/728, 847/845, 1001/1000


POTE generator: ~243/196 = 372.602
==== 2.5.7.13 subgroup ====
Subgroup: 2.5.7.13


Map: [&lt;2 10 27 23 33 31|, &lt;0 -11 -36 -28 -42 -38|]
Comma list: 343/338, 640/637
EDOs: 58, 190, 248, 438d
Badness: 0.0261


</pre></div>
Sval mapping: {{mapping| 1 3 3 4 | 0 -7 -2 -3 }}
<h4>Original HTML content:</h4>
 
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Quince clan&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:6:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;&lt;a href="#Essence"&gt;Essence&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;
Gencom mapping: {{mapping| 1 0 3 3 0 4 | 0 0 -7 -2 0 -3 }}
&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;br /&gt;
 
This tempers out quince, the no-threes comma |-15 0 -2 7&amp;gt; = 823543/819200. Quince temperaments include miracle, quincy, octowerck and birds as well as the ones listed below.&lt;br /&gt;
: gencom: [2 14/13; 343/338 640/637]
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Essence"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Essence&lt;/h1&gt;
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 116.094
Essence is of interest because of the abundant supply of essentially tempered chords.&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 10, 21, 31}}
Commas: 321489/320000, 823543/820125&lt;br /&gt;
 
&lt;br /&gt;
==== 2.5.7.13.17 subgroup ====
POTE generator: ~243/196 = 372.597&lt;br /&gt;
Subgroup: 2.5.7.13.17
&lt;br /&gt;
 
Map: [&amp;lt;2 10 27 23|, &amp;lt;0 -11 -36 -28|]&lt;br /&gt;
Comma list: 170/169, 224/221, 640/637
Wedgie: &amp;lt;&amp;lt;22 72 56 63 27 -72||&lt;br /&gt;
 
EDOs: 58, 190, 248, 438d, 686d&lt;br /&gt;
Sval mapping: {{mapping| 1 3 3 4 4 | 0 -7 -2 -3 1 }}
Badness: 0.1736&lt;br /&gt;
 
&lt;br /&gt;
Gencom mapping: {{mapping| 1 0 3 3 0 4 4 | 0 0 -7 -2 0 -3 1 }}
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Essence-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
 
Commas: 441/440, 8019/8000, 456533/455625&lt;br /&gt;
: gencom: [2 14/13; 170/169 224/221 640/637]
&lt;br /&gt;
 
POTE generator: ~243/196 = 372.599&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.769
&lt;br /&gt;
 
Map: [&amp;lt;2 10 27 23 33|, &amp;lt;0 -11 -36 -28 -42|]&lt;br /&gt;
{{Optimal ET sequence|legend=1| 10, 21, 31 }}
EDOs: 58, 190, 248, 438d&lt;br /&gt;
 
Badness: 0.0464&lt;br /&gt;
==== 2.5.7.13.17.19 subgroup ====
&lt;br /&gt;
Subgroup: 2.5.7.13.17.19
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Essence-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
 
Commas: 441/440, 729/728, 847/845, 1001/1000&lt;br /&gt;
Comma list: 170/169, 343/338, 640/637, 16384/16055
&lt;br /&gt;
 
POTE generator: ~243/196 = 372.602&lt;br /&gt;
Sval mapping: {{mapping| 1 3 3 4 4 3 | 0 -7 -2 -3 1 13 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 10 27 23 33 31|, &amp;lt;0 -11 -36 -28 -42 -38|]&lt;br /&gt;
Gencom mapping: {{mapping| 1 0 3 3 0 4 4 3 | 0 0 -7 -2 0 -3 1 13 }}
EDOs: 58, 190, 248, 438d&lt;br /&gt;
 
Badness: 0.0261&lt;/body&gt;&lt;/html&gt;</pre></div>
: gencom: [2 14/13; 170/169 343/338 640/637 16384/16055]
 
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.716
 
{{Optimal ET sequence|legend=1| 10, 21, 31, 52f }}
 
[[Category:Temperament clans]]
[[Category:Pages with mostly numerical content]]
[[Category:Quince clan| ]] <!-- main article -->
[[Category:Quince| ]] <!-- key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Quince_clan"